Question

the math behind nye in times square
each year on new year’s eve thousands of people come to times square in new york city to watch a large sparkling ball drop, signifying a new year has begun. below you will find questions relating to the big night. find the answer to each of the facts about new year’s eve in times square by completing the math problem in each box. remember to show your work and include the unit for each answer.

1. how many times will the ball have dropped in times square since nye 1908?

$5^2 + 2^5 + (5 \times 10) + 2^3 + 1^6$

1. what is the weight(in pounds) of the current ball that is dropped each year?

$475 \times 25$

1. how many different balls have been used since 1908?

find the quotient of 2,247 and 321.

1. how many tiny
2. how long does it
3. how many

Explanation:

Problem 1:

Step 1: Calculate each term

• \(5^2 = 25\)
• \(2^5 = 32\)
• \(5\times10 = 50\), so \((5\times10)=50\)
• \(2^3 = 8\)
• \(1^6 = 1\)

Step 2: Sum all terms

\(25 + 32 + 50 + 8 + 1\)
First, \(25+32 = 57\)
Then, \(57+50 = 107\)
Then, \(107+8 = 115\)
Then, \(115+1 = 116\)

Step 1: Multiply 475 and 25

\(475\times25=(400 + 75)\times25\)
Using distributive property: \(400\times25+75\times25\)
\(400\times25 = 10000\)
\(75\times25=\frac{75\times100}{4}=1875\) (or directly \(75\times25 = 1875\))

Step 2: Sum the results

\(10000+1875 = 11875\)

Step 1: Divide 2247 by 321

We know that \(321\times7 = 2247\) (because \(321\times5 = 1605\), \(321\times6 = 1926\), \(321\times7=2247\))

Answer:

116

Problem 2: